Methods and apparatuses disclosed herein provide beam hardening correction to tomographic reconstruction using a simplification to the Alvarez-Macovski attenuation model. An example method includes simplifying a forward projection model, the forward projection model based on an Alvarez-Macovski (AM) attenuation model, wherein the simplification of the forward projection model simplifies the AM attenuation model for one of photoelectric effect only, constant density, constant atomic number, and density proportional to atomic number, and performing an iterative reconstruction of a sample using the simplified forward projection model, the iterative reconstruction weighted by a first spectrum, wherein measured image data of the sample used in the iterative reconstruction is obtained at a first energy, and wherein a reverse operation of the iterative reconstruction is a non-adjoint to the simplified forward projection model.
Legal claims defining the scope of protection, as filed with the USPTO.
1. A method for tomographic image reconstruction of a sample, the method comprising: simplifying a forward projection model, the forward projection model based on an Alvarez-Macovski (AM) attenuation model, wherein simplifying of the forward projection model includes simplifying the AM attenuation model for one of photoelectric effect only, constant density throughout the sample, constant atomic number throughout the sample, and density proportional to atomic number; and performing an iterative reconstruction of the sample using the simplified forward projection model and a back projection, wherein measured image data of the sample obtained at a first energy is compared with an output of the simplified forward projection weighted by a first spectrum associated with the first energy, and wherein the back projection of the iterative reconstruction is non-adjoint to the simplified forward projection model, and wherein the back projection assuming monochromatic radiation.
2. The method of claim 1 , wherein the simplification of the forward projection model for photoelectric effect only comprises ignoring a Compton scattering effects term in the AM attenuation model so that only the photoelectric effect term is implemented.
3. The method of claim 1 , wherein the simplification of the forward projection model for constant density comprises projecting the AM attenuation model with density set at a constant.
4. The method of claim 1 , wherein the simplification of the forward model for constant atomic number comprises projecting the AM attenuation model with atomic number set at a constant.
5. The method of claim 1 , wherein the simplification of the forward model for density proportional to atomic number comprises setting atomic number to the density sample parameter weighted by a proportionality constant and substituting for atomic number in the AM attenuation model.
6. The method of claim 1 , wherein simplifying a forward projection model comprises reducing a number of variables from two to one, wherein the two variables include density and atomic number, and wherein reducing the number of variables includes making density a function of atomic number or making atomic number a function of density.
7. The method of claim 1 , further comprising: determining the simplification of the AM attenuation model based on determining the simplification that minimizes residual error in performing the iterative reconstruction.
8. The method of claim 1 , wherein performing the iterative reconstruction of the sample using the simplified forward projection model reduces beam hardening artifacts in the reconstruction.
9. The method of claim 1 , wherein high energy data of the sample obtained from a high energy, low resolution scan is used to determine the simplification and beginning density and atomic number values used in the iterative reconstruction.
10. The method of claim 1 , wherein low energy, high resolution data of the sample is used in the iterative reconstruction.
11. A system comprising: a stage for mounting a sample; an x-ray source coupled to provide x-rays for imaging the sample; a detector coupled to receive the x-rays after traversing the sample; and a controller coupled at least to the x-ray source and the detector, the controller including or coupled to one or more processors configured to execute code stored on a memory that when executed causes the controller to: simplify a forward projection model, the forward projection model based on an Alvarez-Macovski (AM) attenuation model, wherein simplify the forward projection model includes simplify the AM attenuation model for one of photoelectric effect only, constant density throughout the sample, constant atomic number throughout the sample, and density proportional to atomic number; and perform an iterative reconstruction of the sample using the simplified forward projection model and a back projection, wherein measured image data of the sample obtained at a first energy is compared with an output of the simplified forward projection weighted by a first spectrum associated with the first energy, and wherein the back projection of the iterative reconstruction is non-adjoint to the simplified forward projection model, and wherein the back projection assuming monochromatic radiation.
12. The system of claim 11 , wherein the code for executing the simplification of the forward projection model for photoelectric effect only further includes code, that when executed, causes the controller to ignore a Compton scattering effects term in the AM attenuation model so that only the photoelectric effect term is implemented.
13. The system of claim 11 , wherein the code for executing the simplification of the forward projection model for constant density further includes code, that when executed, causes the controller to project the AM attenuation model with density set at a constant.
14. The system of claim 11 , wherein the code for executing the simplification of the forward model for constant atomic number density further includes code, that when executed, causes the controller to project the AM attenuation model with atomic number set at a constant.
15. The system of claim 11 , wherein the code for executing the simplification of the forward model for density proportional to atomic number density further includes code, that when executed, causes the controller to set atomic number to the density sample parameter weighted by a proportionality constant and substituting for atomic number in the AM attenuation model.
16. The system of claim 11 , wherein the code to simplify a forward projection model further includes code, that when executed, causes the controller to reduce a number of variables from two to one, wherein the two variables include density and atomic number, and wherein reducing the number of variables includes making density a function of atomic number or making atomic number a function of density.
17. The system of claim 11 , further including code that when executed, causes the controller to: determine the simplification of the AM attenuation model based on determining the simplification that minimizes residual error in performing the iterative reconstruction.
18. The system of claim 11 , wherein to perform the iterative reconstruction of the sample using the simplified forward projection model reduces beam hardening artifacts in the reconstruction.
19. The system of claim 11 , wherein the code, when executed by the one or more processors, causes the controller to obtain high energy data of the sample from a high energy, low resolution scan, and further cause the high energy data to be used to determine the simplification and beginning density and atomic number values used in the iterative reconstruction.
20. The system of claim 11 , wherein low energy, high resolution data of the sample is used in the iterative reconstruction.
Cooperative Patent Classification codes for this invention. Click any code to explore related patents in that topic.
August 23, 2018
January 26, 2021
Browse 5M+ US patents with plain-English claim translations and AI-generated analysis.